From Robotics to Sepsis Treatment: Offline RL via Geometric Pessimism

Offline Reinforcement Learning (RL) promises the recovery of optimal policies from static datasets, yet it remains susceptible to the overestimation of out-of-distribution (OOD) actions, particularly in fractured and sparse data manifolds. Current solutions necessitate a trade-off between computational efficiency and performance. Methods like CQL offer rigorous conservatism but require tremendous compute power while efficient expectile-based methods like IQL often fail to correct OOD errors on pathological datasets, collapsing to Behavioural Cloning. In this work, we propose Geometric Pessimism, a modular, compute-efficient framework that augments standard IQL with density-based penalty derived from k-nearest-neighbour distances in the state-action embedding space. By pre-computing the penalties applied to each state-action pair, our method injects OOD conservatism via reward shaping with a O(1) training overhead to the training loop. Evaluated on the D4RL MuJoCo benchmark, our method, Geo-IQL outperforms standard IQL on sensitive and unstable medium-replay tasks by over 18 points, while reducing inter-seed standard-deviation by 4 times. Furthermore, Geo-IQL does not degrade performance on stable manifolds. Crucially, we validate our algorithm on the MIMIC-III Sepsis critical care dataset. While standard IQL collapses to behaviour cloning, Geo-IQL demonstrates active policy improvement. Maintaining safety constraints, it achieves 86.4% terminal agreement with clinicians compared to IQL's 75%. Our results suggest that geometric pessimism provides the necessary regularisation to safely overcome local optima in critical, real-world decision systems.